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In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
We discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity…
A previous knowledge of the domains of dependence of an Hamilton Jacobi equation can be useful in its study and approximation. Information of this nature are, in general, difficult to obtain directly from the data of the problem. In this…
In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This HJB equation is related to a stochastic optimal control problem for which…
Maintaining confidential information control in software is a persistent security problem where failure means secrets can be revealed via program behaviors. Information flow control techniques traditionally have been based on static or…
Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However,…
This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in metric spaces.…
Within a robot autonomy stack, the planner and controller are typically designed separately, and serve different purposes. As such, there is often a diffusion of responsibilities when it comes to ensuring safety for the robot. We propose…
Language-based information flow security aims to decide whether an action-observable program can unintentionally leak confidential information if it has the authority to access confidential data. Recent concerns about declassification…
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a…
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function…
We give a new perspective on the existence of viscosity solutions for a stationary and a time-dependent first-order Hamilton-Jacobi equation. Following recent comparison principles, we work in a framework in which we consider a subsolution…
Side-channel attacks that leak sensitive information through a computing device's interaction with its physical environment have proven to be a severe threat to devices' security, particularly when adversaries have unfettered physical…
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous…
We study an agency problem between a leader (the principal) seeking to design an optimal incentive scheme to a follower (the agent) to increase the value of a risky project subjected to accidents and volatility uncertainty. The agency…
In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…
As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult.…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf…